A096786 Numbers n such that both n and n+1 are composite numbers that sum up to a Pythagorean prime (i.e., of the form 4k+1).

8, 14, 20, 26, 44, 48, 50, 54, 56, 68, 74, 86, 90, 98, 114, 116, 120, 128, 134, 140, 146, 158, 168, 174, 176, 186, 194, 200, 204, 216, 224, 230, 254, 260, 278, 284, 288, 296, 300, 308, 320, 326, 338, 350, 354, 380, 384, 386, 398, 404, 410, 414, 426, 428, 440

Offset

1,1

Links

Table of n, a(n) for n=1..55.

Formula

Equals (A096785 - 1)/2.

Mathematica

Select[ Range[450], PrimeQ[ # ] == PrimeQ[ # + 1] == PrimeQ[2# + 1, GaussianIntegers -> True] == False && PrimeQ[2# + 1] == True &] (* Robert G. Wilson v, Jul 11 2004 *)

Prog

(PARI) nextcomposite(k)=if(k<3, 4, if(isprime(k), k+1, k));
{m=465; n=4; while(n<m, k=nextcomposite(n+1); p=n+k; if(k==n+1&&isprime(p)&&p%4==1, print1(n, ", ")); n=k)} \\ Klaus Brockhaus, Jul 11 2004

Crossrefs

Subsequence (even numbers) of A096784. See A096785 for the associated primes.

Cf. A060254, A096784, A096785, A096787, A096788, A096675.

Sequence in context: A091572 A369644 A369659 * A114527 A345089 A200328

Adjacent sequences: A096783 A096784 A096785 * A096787 A096788 A096789

Keyword

nonn

Author

Lekraj Beedassy, Jul 09 2004

Extensions

Corrected and extended by Klaus Brockhaus, Rick L. Shepherd and Ray Chandler, Jul 10 2004

Status

approved